The leader of the Catholic Church in England and Wales told Anglican leaders that "new tensions" delayed unity, but they were about very important issues.
The ordination of gay Anglican bishops has dominated the Lambeth conference of hundreds of Anglican leaders.
The archbishop added: "Our future dialogue will not be easy until such fundamental matters are resolved".
Addressing the conference, held every 10 years, Cardinal Murphy-O'Connor said he took "no pleasure at all to see the current strains in your communion".
Gay bishops
More than 220 traditionalist bishops have boycotted the conference and the Archbishop of Sudan, Daniel Deng, has called for the openly gay American bishop, Gene Robinson, to resign and go back to being "a normal Christian".
Cardinal Murphy-O'Connor said the work of unity between the Catholic and Anglican church during the past 40 years has come "complete with all the challenge that your treasured (Anglican) diversity can sometimes bring to the table."
He also acknowledged that the Catholic Church has experienced problems over the ordination of women - a problematic issue as Anglicans do ordain women.
Cardinal Murphy-O'Connor said he was "not gloomy" about the future but said: "If anybody ever thought that such questions concerned only the individual conscience and had little ecclesial (let alone ecumenical) consequence, events have shown otherwise."
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